The D&D Adventurers League Player's Pack includes a "Content Catalog", that details all the available adventure sources and what the appropriate level band is. The content catalog is the authoritative document.
As of v7.03a, "Lost Mine of Phandelver" (otherwise known as DDHC-LMOP) has a level band of 1-4. Phandelver being classified as a "hardcover" (that's what DDHC means) indicates that any character within the level range can start the content, but are not kicked out if they breach the listed range1. A character outside the listed range for a hardcover can't start it, but can finish one they started while in-range.
Other Introductory Material
The introductory modules (which group five one-hour mini modules together) are generally the only modules with a restricted level band that doesn't match a tier. In seasons one through five, they were restricted to L1 and L2. Season 6 was handled a little differently - a slice of the HC instead of mini-modules. In fact, the Season Six hardcover itself, Yawning Portal, is a bit of an aberration, but the content catalog details the differences. Season 7's mini-modules are full Tier 1 (L1 through L4).
1In DDAL play, it's possible to play modules while still involved in an on-going hardcover group, leveling up at a different time than other players in the same hardcover group might.